Light weight structural materials in the form of lattices and foams are attractive to engineers due to their efficient use of constituent materials. Foams and lattices can have high stiffnesses, strengths, and energy absorption capabilities relative to the amount of solid material in the system. These materials are generally known as cellular materials. They find particular utility as the core materials for hybrid structures as cushioning, thermal insulation, and in energy absorbing structures, such as helmets and packaging used in shipping. Their properties are derived largely from the geometric arrangement of the constituent materials. Most commonly this arrangement is on a length scale that is small compared to the part or device to which they are attached and large compared to the microstructure of the constituent material.
Cellular materials are ubiquitous in engineered systems due to the wide range of properties they exhibit. They can be formed from a wide variety of materials including stiff and flexible polymers, ductile metals, and ceramics. The intrinsic properties of the constituent material, such as thermal and electrical conductivity, are inherited, although modified by the geometry of the cell. Cellular geometries exist in a space ranging from open to closed cell and random to ordered. Lattices are open cell ordered structures, for example. The stiffness and strength of cellular materials vary with their position in this space as various arrangements of beam and plate members. Closed cell stochastic (random) foams are known to have a higher specific stiffness (stiffness per unit mass of constituent material) than open cell random foams. This is in part due to the constraint that cell faces place on the deformation of cell edges, greatly limiting the available modes of deformation, in are what otherwise bending dominated structures. Lattices are known to outperform closed cell random foams, also because there is less bending of material. Stress and strain energy is relatively well distributed in aligned members leading to higher performance. Closed cell ordered foams have the highest potential performance, due to the alignment and constraint of material. Cell edges are aligned similarly to lattices and have the added support of cell faces, which are also aligned. These closed cell ordered materials have the unique ability, due to contribution from multiple factors, to achieve theoretical upper bounds for stiffness
Ordered foams, in the form of honeycombs, are widely used in engineered systems but possess inherent anisotropy due to their two-dimensional (2-D) geometry. Complex three-dimensionally (3-D) aligned materials can now be practically developed with the advent of 3-D printing and other modern automated assembly techniques, referred to generally as direct manufacturing, additive manufacturing, or rapid prototyping. These techniques can be used to fabricate closed cell highly aligned materials of virtually any geometry, including isotropic designs. Isotopic, or non-directional, material properties are advantageous in many applications where loads are multi-axial (multi-directional), or simply to avoid the complexity of designing with anisotropic materials. Direct manufacturing allows for the production of complex cellular materials.
Direct manufacturing removes much of the cost associated with fabricating complex designs. In traditional machining techniques and bonding methods, such as brazing and welding, the level of complexity builds as the part is manufactured. Parts begin as a simple billet block or with pairs of members to be bonded. Features are then added, with tool passes to remove material or bonded by welding, adhesives, brazing or other methods to join material. Each tool pass and weld has an associated cost that increases with the complexity of the part. With direct manufacturing the complexity is inherent, with no additional associated cost. Fabricating large monolithic parts, like the geometry of a billet block, requires the most time and cost in these types of techniques, low density efficient materials the least. Historically, honeycombs and lattice have been limited to high end applications such as aviation and space due to their high cost. With this cost mitigated by direct manufacturing such ordered materials can now find much wider use to the benefit of both producers and users of manufactured goods. The question then becomes that of identifying material geometries that utilize the printed constituent materials in the most efficient way.
What is presented are material cellular geometries that achieve a very large portion of theoretical upper bounds for stiffness and that can be used to create cell structures that can further take advantage of the benefits provided by direct manufacturing methods.